BAGHDAD (AP) — Iran and six world powers wrapped up talks Thursday still far apart over how to oversee Tehran’s atomic program, but with resolve to keep dialogue going as an alternative to possible military action.

Envoys said they will meet again next month in Moscow after negotiations stretched out for extra hours and a sandstorm shut the airport in Iraq’s capital. But the two sides agreed on little else during two dramatic days of discussions that underscored the serious challenges of reaching accords between Iran and the West.

“It is clear that we both want to make progress, and that there is some common ground,” European Union foreign policy chief Catherine Ashton, who is formally leading the talks, told reporters. “However, significant differences remain. Nonetheless, we do agree on the need for further discussion to expand that common ground.”

Saeed Jalili, Iran’s top nuclear negotiator, offered a lukewarm assessment of what the negotiations achieved, in light of European and American refusal to lift tough sanctions as Tehran had hoped.

“The result of the talks was that we were able to get more familiar with the views of each other,” Jalili said at a press conference after Ashton left.

The Baghdad discussions began with hopes for progress before each side accused the other of failing to offer meaningful, realistic proposals. More tellingly, they also showed that U.S. diplomats and others are pressing neither for quick deals nor for ultimatums that could derail the sensitive talks.

“We are moving in a step-by-step process,” a senior American official told reporters in Baghdad’s heavily protected Green Zone. “It’s good for them. It’s good for us. It’s good for the world.”

The tempered approach offers insights into shifting American priorities over Iran’s nuclear ambitions.

The U.S. has gradually moved off its demands for an immediate and complete halt to Iran’s ability to make nuclear fuel, which the West and allies fear could someday provide the foundations of warhead-grade material. Iran denies it seeks atomic arms.

Instead, the Baghdad talks unveiled a Western-backed incentive package that seeks to end Iran’s highest-level uranium enrichment as a first step. That leaves open speculation that Washington could ultimately accept Iran’s demand to keep its enrichment labs in operation — although possibly at reduced levels to produce lower-grade fuel suitable for its lone power-generating reactor.

Such a compromise would likely require Iran to reciprocate with moves such as allowing greater U.N. nuclear inspections and suspending work at a bunker-like enrichment site south of Tehran.

The senior U.S. official said it was still “premature” to delve into this type of endgame bargaining. “It’s having the discussion about the end of the road before you’ve taken the first step in the road,” said the official, who spoke on condition of anonymity to discuss the negotiations more candidly.

In Washington, Secretary of State Hillary Rodham Clinton said significant differences remain between the two sides and that it’s now up to Iran “to close the gaps.”

“Iran now has the choice to make: Will it meet its international obligations and give the world confidence about its intentions or not,” Clinton said.

The overall message, however, was somehow to keep talking. The Moscow negotiations are set for June 18-19.

“All parties in the talks want to gain time,” said Bruno Tertrais, a senior researcher at the Foundation for Strategic Research in Paris. “The Western countries want sanctions to keep hitting Iran, and Iran wants to keep the talk of military action in the distance.”

The open channels between Iran and the six-nation bloc — the five permanent Security Council members plus Germany — could push back threats of military action that have shaken oil markets and fostered fears of triggering a wider Middle East conflict.

Israeli leaders, on the other hand, have been highly critical of the talks, claiming it allows Iran to buy time and drive a wedge between Washington and Jerusalem. On Wednesday, Israel’s defense minister, Ehud Barak, said even possible moves by Iran to open its nuclear facilities to greater U.N. inspect don’t rule out a possible Israeli military strike.

The world powers opened the Baghdad talks with a U.S.-backed proposal calling on Tehran to halt the production of 20 percent enriched uranium, which is the highest grade of enrichment that Iran has acknowledged.

In exchange, the world powers offered benefits, including medical isotopes, some nuclear safety cooperation and spare parts for civilian airliners that are needed in Iran.

Staking out a hard-line reply, Iran emphasized it has every right to pursue uranium enrichment for peaceful uses. Jalili said Iran would consider suspending the 20 percent level but only if the world powers recognize its right to enrich uranium.

He also said the West would have to give in to demands to supply Iran with enough nuclear fuel to run a Tehran medical research reactor that currently depends on the 20 percent-level enriched uranium.

“It could be an issue for cooperation over discussions related to the Tehran reactor,” Jalili said.

Western leaders fear the 20 percent-level material — well above the 3.5 percent enrichment needed for energy-producing reactors — can be turned into warhead grade at about 90 percent enrichment in a matter of months. Iran insists its reactors are only for energy and research.

Iran went into the talks urging the West to scale back on recently toughened sanctions, which have targeted Iran’s critical oil exports and have effectively blackballed the country from international banking networks. The 27-nation European Union is set to ban all Iranian fuel imports on July 1, shutting the door on about 18 percent of Iran’s market.

The senior U.S. official predicted the pace of the talks would speed up in upcoming rounds.

“We are urgent about it, because every day we don’t figure this out is a day they keep going forward with a nuclear program,” the official said. “And there are all kinds of assessments about how long it will take them to get there.”

“We still think we have some time for diplomacy, but it’s not indefinite,” he said.

Talks resumed in Istanbul last month more than a year after an attempt at Western dialogue with Iran collapsed.

Iran pushed for the second round in Baghdad as a way to showcase its regional influence and close ties to the Iraqi government after the U.S. military withdrawal from Iraq. During the talks, a mortar strike outside the Green Zone killed at least one person and wounded eight, according to police and medical officials. The level of violence has dropped dramatically in Iraq, although deadly attacks on security forces and civilians are still common.